Scale-invariant Perturbations: Model-independent Analysis of Alternatives to Cosmic inflation
Moradinezhad Dizgah, Azadeh
MetadataShow full item record
The focus of this thesis is to study generation of scale-invariant perturbation in non-inflationary backgrounds. Throughout we assume that the universe is dominated by a single scalar degree of freedom at early times when the perturbations are generated. The first three chapters consist of review materials needed for the follow up discussion in the last three chapters which present our findings. We probe the parameter space of scalar field models first by using the dualities that preserve the form of the horizons relevant for generation of perturbations. For canonical scalar field models, we use a known duality between expanding and contracting cosmologies to construct a dual of the inflationary flow hierarchy applicable to contracting cosmologies such as ekpyrotic and cyclic models. We show that the inflationary flow equations are invariant under the duality and therefore apply equally well to inflation or to cyclic cosmology. We then generalize the cosmological duality between inflation and cyclic contraction to the case of non-canonical scalar field theories with varying speed of sound. The single duality in the canonical case generalizes to a family of three dualities constructed to leave the cosmological acoustic horizon invariant. We find three classes of models: (I) DBI inflation, (II) the non-canonical generalization of cyclic contraction, and (III) a new cosmological solution with rapidly decreasing speed of sound and relatively slowly growing scale factor, which we dub stalled cosmology. We construct dual analogs to the inflationary slow roll approximation, and solve for the curvature perturbation in all three cases. Both cyclic contraction and stalled cosmology predict a strongly blue spectrum for the curvature perturbations inconsistent with observations. Taking a more phenomenological approach, in the last chapter, we investigate the general properties of expanding cosmological models which generate scale-invariant curvature perturbations in the presence of a variable speed of sound. We show that in an expanding universe, generation of a super-Hubble, nearly scale-invariant spectrum of perturbations over a range of wavelengths consistent with observation requires at least one of three conditions: (1) accelerating expansion, (2) a speed of sound faster than the speed of light, or (3) super-Planckian energy density.